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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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Cited by 1107 (16 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
A Correspondence Theory for Terminological Logics: Preliminary Report
 In Proc. of IJCAI91
, 1991
"... We show that the terminological logic ALC comprising Boolean operations on concepts and value restrictions is a notational variant of the propositional modal logic K (m) . To demonstrate the utility of the correspondence, we give two of its immediate byproducts. Namely, we axiomatize ALC and give a ..."
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Cited by 257 (0 self)
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We show that the terminological logic ALC comprising Boolean operations on concepts and value restrictions is a notational variant of the propositional modal logic K (m) . To demonstrate the utility of the correspondence, we give two of its immediate byproducts. Namely, we axiomatize ALC and give a simple proof that subsumption in ALC is PSPACEcomplete, replacing the original sixpage one. Furthermore, we consider an extension of ALC additionally containing both the identity role and the composition, union, transitivereflexive closure, range restriction, and inverse of roles. It turns out that this language, called T SL, is a notational variant of the propositional dynamic logic converse PDL. Using this correspondence, we prove that it suffices to consider finite T SLmodels, show that T SLsubsumption is decidable, and obtain an axiomatization of T SL. By discovering that features correspond to deterministic programs in dynamic logic, we show that adding them to T SL preserves...
Reasoning about The Past with TwoWay Automata
 In 25th International Colloqium on Automata, Languages and Programming, ICALP ’98
, 1998
"... Abstract. The pcalculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the pcalculus is EXPTIMEcomplete. This upp ..."
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Cited by 129 (12 self)
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Abstract. The pcalculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the pcalculus is EXPTIMEcomplete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result in this paper is an exponential time upper bound for the satisfiability problem of the pcalculus with both forward and backward modalities. To get this result we develop a theory of twoway alternating automata on infinite trees. 1
Unifying classbased representation formalisms
 J. of Artificial Intelligence Research
, 1999
"... The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their c ..."
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Cited by 97 (34 self)
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The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts. The proposed formalism is expressed in the style of description logics, which have been introduced in knowledge representation as a means to provide a semantically wellfounded basis for the structural aspects of knowledge representation systems. The description logic considered in this paper is a subset of first order logic with nice computational characteristics. It is quite expressive and features a novel combination of constructs that has not been studied before. The distinguishing constructs are number restrictions, which generalize existence and functional dependencies, inverse roles, which allow one to refer to the inverse of a relationship, and possibly cyclic assertions, which are necessary for capturing real world
Reasoning in expressive description logics with fixpoints based on automata on infinite trees
 In Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI’99
, 1999
"... In the last years, the investigation on Description Logics (DLs) has been driven by the goal of applying them in several areas, such as, software engineering, information systems, databases, information integration, and intelligent access to the web. The modeling requirements arising in the above ar ..."
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Cited by 55 (12 self)
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In the last years, the investigation on Description Logics (DLs) has been driven by the goal of applying them in several areas, such as, software engineering, information systems, databases, information integration, and intelligent access to the web. The modeling requirements arising in the above areas have stimulated the need for very rich languages, including fixpoint constructs to represent recursive structures. We study a DL comprising the most general form of fixpoint constructs on concepts, all classical concept forming constructs, plus inverse roles, nary relations, qualified number restrictions, and inclusion assertions. We establish the EXPTIME decidability of such logic by presenting a decision procedure based on a reduction to nonemptiness of alternating automata on infinite trees. We observe that this is the first decidability result for a logic combining inverse roles, number restrictions, and general fixpoints. 1
Automated Temporal Reasoning about Reactive Systems
, 1996
"... . There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective a ..."
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Cited by 39 (2 self)
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. There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective and reliable means of specifying and ensuring correct behavior of such systems. This paper discusses known complexity and expressiveness results for a number of such logics in common use and describes key technical tools for obtaining essentially optimal mechanical reasoning algorithms. However, the emphasis is on underlying intuitions and broad themes rather than technical intricacies. 1 Introduction There is a growing need for reliable methods of designing correct reactive systems. These systems are characterized by ongoing, typically nonterminating and highly nondeterministic behavior. Examples include operating systems, network protocols, and air traffic control systems. There is w...
Finite model reasoning in description logics
 In Proc. of the 5th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR96
, 1996
"... For the basic Description Logics reasoning with respect to finite models amounts to reasoning with respect to arbitrary ones, but finiteness of the domain needs to be considered if expressivity is increased and the finite model property fails. Procedures for reasoning with respect to arbitrary model ..."
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Cited by 37 (16 self)
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For the basic Description Logics reasoning with respect to finite models amounts to reasoning with respect to arbitrary ones, but finiteness of the domain needs to be considered if expressivity is increased and the finite model property fails. Procedures for reasoning with respect to arbitrary models in very expressive Description Logics have been developed, but these are not directly applicable in the finite case. We first show that we can nevertheless capture a restricted form of finiteness and represent finite modeling structures such as lists and trees, while still reasoning with respect to arbitrary models. The main result of this paper is a procedure to reason with respect to finite models in an expressive Description Logic equipped with inverse roles, cardinality constraints, and in which arbitrary inclusions between concepts can be specified without any restriction. This provides the necessary expressivity to go beyond most semantic and objectoriented Database models, and capture several useful extensions. 1
Regular XPath: Constraints, Query Containment and ViewBased Answering for XML Documents
"... In this paper we consider a powerful mechanism, called Regular XPath, for expressing queries and constraints over XML data, including DTDs and existential path constraints and their negation. Regular XPath extends XPath with binary relations over XML nodes specified by means twoway regular path que ..."
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Cited by 9 (0 self)
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In this paper we consider a powerful mechanism, called Regular XPath, for expressing queries and constraints over XML data, including DTDs and existential path constraints and their negation. Regular XPath extends XPath with binary relations over XML nodes specified by means twoway regular path queries. Our first contribution deals with checking satisfiability of Regular XPath constraints. While this problem could be reduced in terms of reasoning in repeat converse deterministic PDL, a wellknown variant Propositional Dynamic Logic (PDL), the resulting technique would be of little practical use, due to the notorious difficulty of implementing efficient reasoners for such a logic. We therefore propose a direct algorithm for Regular XPath constraints satisfiability, based on checking emptiness of two way alternating automata on finite trees. We show how this algorithm can be implemented symbolically, by using Binary Decision Diagrams (BDDs) as the underlying data structure, which can be significantly more efficient than explicit graphbased algorithms. We then move to query containment and view based query answering for Regular XPath, and show that both problems can be reduced to checking satisfiability of Regular XPath constraints, thus allowing for taking advantage of the techniques developed for constraints satisfiability.